Equivalent Fractions: Reducing Fractions to Simplest Terms Fast And Easy Math Learning Videos
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Title: Equivalent Fractions: Reducing Fractions to Simplest Terms
You’ve already learned how to reduce fractions by rewriting them with a smaller denominator, and you’ve learned how to find the greatest common factor of two numbers.
In this lesson, you’ll put both of these together to rewrite fractions with the smallest possible numbers. This is referred to as “reducing the fraction to simplest terms.” Before we begin, lets’ look at some new words we use when describing fractions.
The first one is term. Term is another way of saying “number”. Five is a term.
Three-fourths is a term.
And two and five-eighths is a term.
When we write a proper or improper fraction, the numerator is a term and the denominator is a term.
When dealing with fractions we also refer to simplest terms or lowest terms. These both mean the same thing. When a fraction is written in simplest terms, or lowest terms, it means the fraction is written with the smallest possible numbers for the numerator and denominator. A fraction is written in simplest terms when the greatest common factor of the numerator and denominator is one.
Here’s an example. Five-twelfths is written in simplest terms. The greatest common factor of 5 and 12 is one. This means neither the numerator nor the denominator can be written with a smaller number.
Another example. Seven-thirds is written in simplest terms. The greatest common factor of the terms is one, so seven and three are the smallest numbers that can be used to write the fraction.
Nine-fourteenths is written in simplest terms. The greatest common factor of the terms is one.
Six-eighths is not written in simplest terms. One is not the greatest common factor of the terms.
This means we can write this fraction with smaller numbers without changing its value. To find the new numerator and denominator, we need the greatest common factor of six and eight. Two is the greatest common factor. We can use two to rewrite the fraction and reduce it to its simplest terms.
We reduce the terms by dividing each term by the greatest common factor, which is 2. When we divide six by two we get three.
And when we divide eight by two we get four.
Three-fourths is the same fraction as six-eighths, but it’s now written in simplest terms.
When we reduce the terms of a fraction using the greatest common factor, we refer to this as “reducing the fraction to simplest terms”. The value of the fraction remains the same, but the numbers used to write it are smaller.
In the remainder of this lesson, you’ll be asked to determine if a fraction is written in simplest terms. If the fraction is not written in simplest terms, you will be asked to reduce the fraction.
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